Low-Temperature Structural Modulations in CdMn7O12, CaMn7O12

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Low-Temperature Structural Modulations in CdMnO , CaMnO , SrMnO , and PbMnO Perovskites Studied by Synchrotron X-ray Powder Diffraction and Mossbauer Spectroscopy 7

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Alexei A. Belik, Yana S. Glazkova, Yoshio Katsuya, Masahiko Tanaka, Alexey V Sobolev, and Igor A. Presniakov J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b01649 • Publication Date (Web): 28 Mar 2016 Downloaded from http://pubs.acs.org on March 29, 2016

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The Journal of Physical Chemistry

Low-Temperature Structural Modulations in CdMn7O12, CaMn7O12, SrMn7O12, and PbMn7O12 Perovskites Studied by Synchrotron X-ray Powder Diffraction and Mössbauer Spectroscopy

Alexei A. Belik,*,† Yana S. Glazkova,†,‡ Yoshio Katsuya,§ Masahiko Tanaka,§ Alexey V. Sobolev,‡ and Igor A. Presniakov‡

†

International Center for Materials Nanoarchitectonics (WPI-MANA), National

Institute for Materials Science (NIMS), Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan. E-mail: [email protected], Tel: +81-29-860-4567 ‡

Department of Chemistry, Lomonosov Moscow State University, Leninskie Gory,

119992 Moscow, Russia. §

Synchrotron X-ray Station at SPring-8, NIMS, Kouto 1-1-1, Sayo-cho, Hyogo 679-

5148, Japan.

1 Environment ACS Paragon Plus


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Abstract

Structural phase transitions in CdMn7O12, CaMn7O12, SrMn7O12, and PbMn7O12 perovskites are investigated by synchrotron X-ray powder diffraction between 113 and 583 K, differential scanning calorimetry (DSC), and Mössbauer spectroscopy on 57

Fe-doped samples. DSC is used to determine phase transition temperatures (TOO).

All the compounds crystallize in space group R-3 at room temperature. An incommensurate structural modulation is observed below TOO = 265 K in SrMn7O12 with a propagation vector q = (0, 0, 0.9235) at 113 K, similar to the already-reported case of CaMn7O12 (with TOO = 258 K and q = (0, 0, 0.9215) at 113 K). However, superstructure reflections of SrMn7O12 are significantly weaker than those of CaMn7O12. On the other hand, a commensurate structural transition is found in CdMn7O12 below TOO = 254 K and in PbMn7O12 below TOO = 294 K; the transition can be described as from space group R-3 to space group P-3 with the same unit cell dimensions (a = 10.43306(2) Å and c = 6.33939(1) Å in CdMn7O12 at 113 K). CdMn7O12 shows quite strong superstructure reflections at 113 K, while PbMn7O12 has extremely small superstructure reflections. Below TOO, the c lattice parameter of all the compounds increases with decreasing temperature (down to 113 K). Mössbauer spectroscopy shows that quadrupole splitting noticeably increases below TOO; and we quantitatively explain this increase in CaMn7O12 by structural modulations. Structure parameters of the R-3 modification and high-temperature Im-3 modification of CaMn7O12 and PbMn7O12 are also reported.


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1. Introduction

ABO3 perovskite-structure compounds are one of the largest families of compounds in inorganic chemistry.1 For an ABO3 compound to crystallize in a perovskite-type structure, the size of A and B cations should be quite different (for example, A = alkali-earth and rare-earth elements and B = 3d-5d transition metals).2 The perovskite structure is usually stable at 0.88 < t < 1.09,1 where t is the Goldschmidt tolerance factor: t = (rA + rO)/[√2(rB + rO)],3 where rA, rB and rO are the ionic radii of the A, B, and oxygen ions, respectively. There is a special class of perovskite-structure materials with the general formula of (AA’3)B4O12 that allows the size of A’ and B cations to be very close to each other.4-10 A perovskite-type structure of (AA’3)B4O12 is stabilized because of a very unusual cation order with 12-foldcoordinated A site and square-coordinated A’ site (actually with four very short A’-O bond lengths, four long A’-O bond lengths, and four very long A’-O bond lengths). Therefore, the A’ site is typically occupied by Jahn-Teller cations, such as, Cu2+ and Mn3+, and most of the (AA’3)B4O12 compounds need high-pressure (HP) and hightemperature (HT) for their preparation. (AA’3)B4O12 materials show many interesting physical and chemical properties,4 for example, low-field magnetoresistence,11 heavy Fermion physics,12 multiferroic behaviour,13,14 and high-performance catalytic activity.15 When A’ = B = Mn, an interesting family of materials is formed, AMn7O12, with (A = Mn,9 Na,16-18 Ca, Cd,16,19 Sr,16,19 Pb,20 La,16,21 Pr,22 Nd,16 and Bi23,24). Many members of this family were discovered in the 1970s by Marezio et al.16,17 and investigated a lot because of complex magnetic-order, orbital-order, and charge-order transitions. Special attention has been given to CaMn7O12 in the literature,13,25-32 probably because CaMn7O12 can be easily prepared at ambient pressure. CaMn7O12 crystallizes in space group R-3 at room temperature (RT) in a charge-ordered (CO) structure;25 and it exhibits a number of structural and magnetic transitions.4 At about TCO = 450-462 K on heating, there is a phase transition to a cubic charge-disordered structure (space group Im-3). An incommensurate structural modulation along the hexagonal c axis takes place below about 250 K,26,27 and it is suggested that the structural modulation is related to orbital ordering (OO), and is crucial in stabilising a chiral magnetic structure below TN1 = 90 K, which breaks inversion symmetry and



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produces electrical polarization.30 There is the second magnetic transition in CaMn7O12 at TN2 = 48 K. The crystal structure of CaMn7O12 has been investigated in a number of papers;25-27 however, structural parameters of the Im-3 modification have not been reported yet. We have recently investigated detailed magnetic and HT structural properties of CdMn7O12 and SrMn7O12.19 The R-3-to-Im-3 transition is found at TCO = 493 K in CdMn7O12 and at TCO = 404 K in SrMn7O12. RT and HT structural properties of PbMn7O12 have been investigated in Ref. 20; however, the resultant Mn-O bond lengths at RT are not consistent with similar Mn-O bond lengths of CdMn7O12, CaMn7O12, and SrMn7O12.19,25,27 There is no information about low-temperature structural phase transitions and structural modulations in CdMn7O12, SrMn7O12 and PbMn7O12. Therefore, in this work, we performed low-temperature synchrotron X-ray powder diffraction and Mössbauer spectroscopy studies of AMn7O12, where CaMn7O12 was investigated as a reference. Structure parameters of the RT R-3 modification and HT Im-3 modification of CaMn7O12 and PbMn7O12 are also reported.

2. Experimental Details

SrMn7O12 was prepared from a stoichiometric mixture of Mn2O3 and 4H-SrMnO3. CdMn7O12 and PbMn7O12 were prepared from stoichiometric mixtures of Mn2O3, ‘MnO1.839’, CdO (99.99 %), and PbO (99.999 %), where ‘MnO1.839’ is commercial ‘MnO2’ (Alfa Aesar, 99.997 %), whose oxygen content was determined to be MnO1.839 (a mixture of Mn2O3 and MnO2). The mixtures were placed in Au capsules and treated at 6 GPa in a belt-type high-pressure apparatus at 1573 K for 2 h for SrMn7O12 and at 1373 K for 2 h for CdMn7O12 and PbMn7O12 (heating rate to the desired temperatures was 10 min). After the heat treatments, the samples were quenched to room temperature (RT), and the pressure was slowly released. The samples were black dense pellets. Single-phase Mn2O3 was prepared from commercial ‘MnO2’ (99.997 %) by heating in air at 923 K for 24 h. Single-phase 4HSrMnO3 was synthesized from a stoichiometric mixture of Mn2O3 and SrCO3 (99.99 %) by annealing in air at 1373 K for 48 h and 1273 K for 24 h.33 CaMn7O12 was prepared from a stoichiometric mixture of Mn2O3 and CaCO3 (99.99 %). The mixture was pressed into pellets and annealed in oxygen at 1223 K for 240 h with four 4 Environment ACS Paragon Plus

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intermediate grindings every 48 h. CdMn6.9657Fe0.04O12, CaMn6.96557Fe0.035O12, and SrMn6.9257Fe0.08O12 were prepared at the same conditions as the undoped samples by adding stoichiometric amounts of Fe2O3 (95.5 % enriched by

57

Fe); the iron-doped

samples crystallize in space group R-3 at RT similar to the undoped samples, and have similar X-ray powder diffraction patterns. X-ray powder diffraction (XRPD) data were collected at RT on a RIGAKU MiniFlex600 diffractometer using CuKα radiation (2θ range of 10−80°, a step width of 0.02°, and a counting time of 1 min/deg). CaMn7O12 and CdMn7O12 contained traces of unidentified impurities; SrMn7O12 contained traces of Mn2O3 impurity; PbMn7O12 contained small amounts of Mn2O3 and Pb3(CO3)2(OH)2 impurities (Figure S1 of Supporting Information). Synchrotron XRPD data were measured between 113 and 583 K on a large DebyeScherrer camera at the BL15XU beam line of SPring-8.34,35 The intensity data were collected between 1° and 60° at 0.003° intervals in 2θ (between 1° and 70° for CaMn7O12 at 490 K); the incident beam was monochromatized at λ = 0.70014 Å. The samples were packed into Lindemann glass capillaries (inner diameter: 0.1 mm), which were rotated during the measurement. Low-temperature experiments started from 113 K, and capillaries with samples were cooled by N2 gas flow. Therefore, at intermediate temperatures, artefact reflections sometimes appeared, mostly from accumulated ice (space group P63/mmc; ICDD PDF Card 42-1142). Regions containing artefact reflections were usually removed from the analysis. The absorption coefficients were also measured. The Rietveld analysis was performed using the RIETAN-2000 program.36 Differential scanning calorimetry (DSC) curves of powder samples were recorded on a Mettler Toledo DSC1 STARe system at a heating/cooling rate of 10 K/min between 173 K and 373 K (423 K for PbMn7O12) in sealed Al capsules. Three runs were performed to check the reproducibility, and very good reproducibility was observed. 57

Fe Mössbauer spectra were recorded between 77 and 450 K using a conventional

constant-acceleration spectrometer. The radiation source 57Co(Rh) was kept at RT. All isomer shifts are referred to α-Fe at 300 K. The experimental spectra were processed and analysed using methods of spectral simulations implemented in the SpectrRelax program.37



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3. Results

3.1. DSC Studies of AMn7O12. In Ref. 19, we observed very strong DSC anomalies in AMn7O12 corresponding to the R-3-to-Im-3 transition at TCO = 493, 462, 404, and 397 K for A = Cd, Ca, Sr, and Pb, respectively. Figure 1 shows DSC curves of AMn7O12 on heating and cooling between 180 and 420 K. Additional weak anomalies were detected at TOO = 254, 258, 265, and 294 K for A = Cd, Ca, Sr, and Pb, respectively, on heating curves. Note that the DSC anomaly was very broad in SrMn7O12 and could be detected/assigned only when compared with other members of the AMn7O12 family; and for a CdMn7O12 sample studied in Ref. 19, TOO was detected at 240 K – this fact shows that variations in real compositions can effect phase transition temperatures. The observed DSC anomalies are intrinsic as confirmed by low-temperature synchrotron XRPD results given below. A baseline of the DSC curves can be more or less unambiguously determined in PbMn7O12, and the estimated enthalpy of the transition is about 0.16 J/g; this value is about 40 times smaller that the enthalpy of the R-3-to-Im-3 transition (6.6 J/g).19 Iron doping had noticeable effects on the DSC anomalies at TCO and TOO reducing the phase transition temperatures and significantly broadening the DSC effects. For example, TCO drops to 479 K in CdMn6.9657Fe0.04O12 and to 379 K in SrMn6.9257Fe0.08O12; and we could detect a very weak anomaly only in CdMn6.9657Fe0.04O12 at TOO ≈ 220 K (Figure S2). 3.2. Synchrotron XRPD Studies of CaMn7O12. Figure 2 gives fragments of experimental synchrotron XRPD patterns of CaMn7O12 at different temperatures. We observed weak satellite reflections, which can be indexed with the propagation vector qp = (0, 0, 0.9215) at 113 K. We used the same propagation vector as in Ref. 26. The incommensurate satellite reflections were broader than the commensurate Bragg reflections. Our results are in perfect agreement with the results reported on CaMn7O12 in the literature.26,27,30 The Ca-O and Mn-O bond lengths (and, therefore, bond valence sum (BVS) values)38 obtained from our RT synchrotron XRPD data (Table 1) are also in perfect agreement with the Ca-O and Mn-O bond lengths obtained from neutron powder diffraction data in the literature.25,30 Therefore, our structural data are highly reliable. Table 2 gives the structural parameters of CaMn7O12 at 490 K in the cubic Im-3 phase since this information is missed in the literature. Experimental, calculated, and difference synchrotron XRPD patterns of


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CaMn7O12 are shown in Figures 3 and S1b. Temperature dependence of the lattice parameters and unit cell volume of CaMn7O12 is given on Figures 4, 5, and S3. The a parameter decreases with decreasing temperature, while the c parameter starts to increase below the incommensurate structural modulation transition. These results are also in agreement with the reported ones.4,31,32 3.3. Synchrotron XRPD Studies of SrMn7O12. Figure 6 gives fragments of experimental synchrotron XRPD patterns of SrMn7O12 at different temperatures. We observed similar incommensurate satellite reflections which can be indexed with the propagation vector qp = (0, 0, 0.9235) at 113 K. However, the satellite reflections of SrMn7O12 were noticeably weaker than those of CaMn7O12. The available lattice parameters of SrMn7O12 are listed in Table 3; the c lattice parameter at 113 K is larger than that at 193 K in agreement with the tendency found in CaMn7O12. Table S1 (Supporting Information) gives the structural parameters of SrMn7O12 at 113 and 295 K in the non-modulated R-3 model from the current synchrotron XRPD data. Experimental, calculated, and difference synchrotron XRPD patterns of SrMn7O12 are shown in Figure S1c and S1d. Note that Mn2O3 impurity becomes clearly orthorhombic at low temperatures.39 3.4. Synchrotron XRPD Studies of CdMn7O12. Figure 7 gives fragments of experimental synchrotron XRPD patterns of CdMn7O12 at different temperatures. We observed many quite strong satellite reflections at 113 K (about 50 reflections at 2θ range of 3−42°). All the satellite reflections can be indexed with the lattice parameters of a = 10.43306(2) Å and c = 6.33939(1) Å and in space group P-3 (No. 147) (Figure S4). In other words, the RT lattice dimensions do not change during the lowtemperature phase transition in CdMn7O12; and a structural modulation can be called commensurate. The available lattice parameters of CdMn7O12 are listed in Table 3, and temperature dependence of the lattice parameters and unit cell volume is shown on Figures 4, 5, and S3. Temperature dependence of the a lattice parameter of CdMn7O12 clearly exhibits a kink near the phase transition temperature; this feature has not been observed in CaMn7O12.4,31,32 Probably, more detailed studies of CaMn7O12 will be needed. The c lattice parameter of CdMn7O12 starts to increase on cooling below the R-3-to-P-3 transition similar to the case of CaMn7O12. The unit cell volume of CdMn7O12 changes smoothly without clear jumps at the phase transition temperatures of 254 K (P-3-to-R-3) and 493 K (R-3-to-Im-3).



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3.5. Synchrotron XRPD Studies of PbMn7O12. A commensurate structural transition from R-3 to P-3 was also found in PbMn7O12 (Figure 8). However, we observed just about 10 satellite reflections at 113 K (at 2θ range of 3−42°), and the intensities of the satellite reflections were significantly weaker than those of CdMn7O12. Superstructure reflections with (h k 0) indexes looked narrower than those with (h k l) indexes; and there was an extremely small shift of (h k l) superstructure reflections (for example, (1 4 2) and (3 3 2) reflections) from their expected positions suggesting a possible extremely small incommensurate modulation. Because the reported Mn-O bond lengths of PbMn7O12 (for example, Mn2-O = 1.98-2.00 Å for the Jahn-Teller distorted Mn2 site and Mn3-O2 = 1.99 Å)20 at RT are not consistent with similar Mn-O bond lengths of CdMn7O12, CaMn7O12, and SrMn7O12 we reinvestigated the crystal structure of PbMn7O12 at 295 and 420 K. The structure parameters are summarized in Tables 1, 2, and S2 (at 113 K in the non-modulated R-3 model); and experimental, calculated, and difference synchrotron XRPD patterns of PbMn7O12 are shown in Figure S1e, S1f, and S1g. Our structural parameters give PbO and Mn-O bond lengths that are in agreement with other members of the AMn7O12 family. The c lattice parameter at 113 K is slightly larger than that at 295 K in agreement with the tendency found in other members of the AMn7O12 family (Table 3). 3.6. Mössbauer Spectroscopy. To obtain additional information about the nature of changes in the local structure of AMn7O12 at the low-temperature structural phase

transitions,

we

performed

Mössbauer

spectroscopy

studies

of

CdMn6.9657Fe0.04O12, CaMn6.96557Fe0.035O12, and SrMn6.9257Fe0.08O12. Figure 9 shows paramagnetic Mössbauer spectra recorded upon decreasing temperature. Mössbauer spectra at all temperatures were described as a superposition of two quadrupole doublets, Fe1 and Fe2, with very close isomer shifts δ1 ≈ δ2 and different quadrupole splittings, ∆1 > ∆2 (Table 4).40,41 The Fe1 doublet corresponds to Fe3+ ions located at the Mn2 site having a strong Jahn-Teller distortion and occupied by Mn3+ ions (Table 1). The Fe2 doublet corresponds to Fe3+ ions located at the Mn3 site having almost symmetrical octahedral coordination and occupied by Mn4+ ions (Table 1).19,40,41 In the P-3 phase of CdMn7O12, the Mn2 site (9d in R-3) will split into 3f and 6g, and the Mn3 site (3b in R-3) – into 1b and 2d.


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Temperature dependence of isomer shifts, δ1(T) and δ2(T), for all the samples is almost linear between 80 and 300 K (Figure S5) without any anomalies (e.g., changes in slope) indicating the absence of any changes in the lattice dynamics. δ1(T) and

δ2(T) show a weak decrease with increasing temperature as expected from the variation of the second-order Doppler (SOD) shift.42 Therefore, the isomer shifts for both Fe1 and Fe2 doublets remain unaffected by the structural transitions indicating that neither the average electron density on iron nuclei nor the SOD shift are sensitive to the transitions. Temperature dependence of quadrupole splitting, ∆1(T) and ∆2(T), deduced from least-squares fitting are given on Figure 10 (the upper part). Quadrupolar interactions represent local distortions via the electric field gradient (EFG) tensor V.43 It is important to note that in the case of high-spin Fe3+(3d5) ions, all the 3d orbitals are half-filled, and Fe3+ ions have no valence contributions to the EFG tensor; therefore, the EFG tensor is mainly determined by the lattice contribution, Vlat. Thus, when Fe3+ ions are located at the Mn2O6 and Mn3O6 octahedra quadrupole splitting of Fe3+ will reflect the corresponding octahedral distortions. In the temperature range from TOO to 300 K, the quadrupolar couplings for both subspectra are almost constant, that is, it reflects a static distortion of the lattice on a time scale of ∼10-7-10-8 s. Below TOO, the overall temperature dependences ∆1(T) and ∆2(T) exhibit a gradual increase (Figure 10). In order to clarify this increase we first obtained theoretical curves, ∆th1(T) and

∆th2(T), using a semi-empirical relation:44 ∆th(T) = ∆(0)(1 - BT3/2)

(1)

where ∆(0) is a saturated value of quadrupole splitting, B is a positive parameter [to reproduce the decrease of the observed quadrupolar coupling constant with increasing temperature]. In our case, these parameters were estimated by fitting of the experimental values of ∆1(T) and ∆2(T) between TOO and 300 K. The resulting ∆(0) and B parameters are summarized in Table S3. The lower part of Figure 10 shows the ∆iexp(T) - ∆ith(T) curves for the Fe1 and Fe2 doublets (∆iexp(T) ≡ ∆i(T)). This plot clearly visualizes changes of quadrupole splitting below TOO, where quadrupole splitting for the Fe2 doublet exhibits the largest

deviation.

Figure

S6

presents

this

effect

in

more

details

for

CaMn6.96557Fe0.035O12, where an unresolved Fe2 doublet at 300 K (∆2 ≈ 0.10 mm/s) gradually transforms to a resolved doublet with ∆2 = 0.26 mm/s at 90 K. In addition, 9 Environment ACS Paragon Plus


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we found no hysteresis between 90 and 300 K in contrast to clear hysteresis observed near 420 K due to a first-order structural phase transition associated with charge ordering: 3Mn3+ + Mn4+ ↔ 4Mn3.25+ (TCO ≈ 420 K).40,41 The same behavior was observed for the samples with A = Sr and Cd showing the similarity of their local structures. In what follows below, we tried to quantitatively explain the ∆1(T) and ∆2(T) dependence using experimental crystal structures of CaMn7O12. The observed behavior of ∆1(T) and ∆2(T) suggests that parameters of the EFG tensor (or the Vlat(T) contribution) for the different Mn sites noticeably change below TOO. The orbital ordering in CaMn7O12 below TOO induces a modulation of atomic positions with a vector t having only one component along the hexagonal c axis.30 Using the notation from Refs. 26 and 45, the atomic position modulation, ui, for an atom i can be described with second-order Fourier coefficients: ui(t) = ui0 + Aisin(2πt) + Bicos(2πt) + li

(2)

where Ai and Bi denote the Fourier second-order coefficients (modulation amplitudes), ui0 is the atomic positions without modulation, li is a lattice translation, and t = q(ui0 + li) is an internal coordinate in the average crystal structure of superspace group R-3(00γ)0 (q denotes a wave vector of the time independent standing wave leading to the modulation). Thus obtained atomic coordinates for CaMn7O12 were used to calculate components {Vij}i,j = x,y,z of the EFG tensor taking into account only ionic monopole-point contributions from the k-th ion:

Vij = ∑ Z k ( 3uik u jk − δijrk2 )rk−5

(3)

k

where Zk is the charge, xik and xjk are the Cartesian coordinates of the k-th ion with a distance rk from the origin located at a given site, and δij is the Kronecher index. We assumed formal oxidation states of ions in CaMn7O12. The calculated contributions to the

EFG

tensor

were

diagonalized,

and

the

resulting

principal

values

|Vzz| ≥ |Vxx| ≥ |Vyy| were used to calculate theoretical quadrupole splitting: ∆mod = (1 γ∞)eQVzz/2(1 + η2/3)1/2, where η ≡ (Vxx – Vyy)/Vzz is the parameter of asymmetry of the EFG tensor, γ∞ = -9.1 denotes the Schterheimer antishielding factor, and Q = 0.15 barns is the quadrupole moment of 57Fe nuclei.43 Calculated values of ∆1mod and ∆2mod for different locations of the Mn2 and Mn3 atoms along the hexagonal c axis at different temperatures are shown in Figure 11a. For the EFG tensor with axial


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symmetry (η ≈ 0), ∆mod(t) can be expended, similar to ui(t) (see equation 2), into harmonics as follows:46

∆mod(t) = ∆0 + A(2)sin(2πt) + B(2)cos(2πt) + A(4)sin(4πt) + B(4)cos(4πt)

(4)

where ∆0 stands for quadrupole splitting without modulation, and A(n) and B(n) denote amplitudes of subsequent Fourier harmonics. As seen in Figure 11a, profiles of

∆1mod(t) and ∆2mod(t) significantly differ from the periodic dependence of Mn-O bond lengths in CaMn7O12.26,30,45 This result is explained by the fact that the resulting main components Vzz(t) of the EFG tensor are a superposition of the partial contributions of the individual ions in the crystal lattice. The EFG tensor distribution p(∆), seen by resonant 57Fe3+ ions, can be calculated using all relevant amplitudes in equation 4: π /2

p ( ∆) ~

∫ d θ δ ( ∆ − ∆0 + A

( 2)

sin(2 θ) + B (2) cos(2 θ) + A(4) sin(4 θ) + B (4) cos(4 θ)) (5)

0

where δ(f(θ)) is the Delta function, f(θ) ≡ ∑ n =1[ A( 2 n ) sin( 2nθ) + B (2 n ) cos( 2nθ)] , and θ 2

≡ 2πt. According to Ref. 45, defining sin(θi) ≡ ξi and transforming function f(θi) → h(ξi), we get:

p ( ∆) ~ ∑ i

1 1 2 1/ 2 ' (1 − ξ i ) h (ξ i )

(6)

where ξi is real solutions of equation 6 on the interval [0,1] and h′(ξi) denotes derivative of the function h(ξi) at the points ξi. Profiles of calculated distributions pi(∆) and corresponding average values of the quadrupole splittings = 1/n∑{pi(∆)×∆i} at different temperatures are shown in Figure 11b. The average values of the quadrupole splitting, and , are plotted as functions of temperature on Figure 10 by red symbols. Because modulated structures have not been reported yet for CdMn7O12 and SrMn7O12 similar calculations could not be performed for them.

4. Discussion All AMn7O12 with A2+ = Cd, Ca, Sr, and Pb crystallize in space group R-3 at RT, and they have a HT structural phase transition from R-3 to Im-3.19 Using the present results, we showed that they also have low-temperature structural modulations.



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However, the structural modulations are very different. The modulations are incommensurate in CaMn7O12 and SrMn7O12 with the surprisingly similar propagation vectors despite quite different sizes of Ca2+ (rXII = 1.34 Å) and Sr2+ (rXII = 1.44 Å) cations.48 On the other hand, the modulations are commensurate in CdMn7O12 with the smaller Cd2+ cation (rXII = 1.31 Å) and with larger Pb2+ cation (rXII = 1.49 Å). This behaviour is difficult to rationalize qualitatively. But it will be interesting to see the effect of different structural modulations on magnetic structures, magnetic moment

modulations,

and

the

emergence

of

electric

polarization.

The

incommensurate modulation is described in space group R-3(00γ)0.26 It is sometimes difficult to treat an incommensurate modulation in first-principle calculations.49 Therefore, the commensurate modulation of CdMn7O12 and PbMn7O12 can serve as a good model in first-principle calculations for understanding multiferroic properties of AMn7O12.50 Independent of the type of modulations, the c lattice parameter decreases with increasing temperature in the modulated phases between (at least) TN1 and TOO. This behavior is clear in CdMn7O12 and CaMn7O12 (Figure 4 and Ref. 32), and less pronounced in SrMn7O12 and PbMn7O12, which show very weak modulated reflections, and where the c parameter is almost constant.19 Therefore, this behavior should be connected with the temperature evolution of an orbital-ordering pattern. In AMn7O12, an unusual Jahn-Teller distortion is observed: the Mn2O6 octahedron is an apically contracted octahedron in comparison with usually observed apically elongated octahedra. The shortest Mn2-O1 bonds are aligned almost along the c axis. Precise temperature evolution of structural parameters (obtained preferably with neutron diffraction) and Mn-O bond lengths and Mn-O-Mn bond angles is needed to understand temperature dependence of the lattice parameters. The temperature of the R-3-to-Im-3 transition gradually decreases with increasing the radius of the A2+ cation with a gap of about 100 K between CdMn7O12 (TCO = 493 K) and PbMn7O12 (TCO = 397 K). On the other hand, the structural modulation transition temperature slightly increases with increasing the radius of the A2+ cation and does not show such a large gap (TOO = 254 K for CdMn7O12 and TOO = 294 K for PbMn7O12). In other words, TCO and TOO are approaching each other in PbMn7O12; it is interesting that TN2 = 78 K and TN1 = 82 K are also merging in PbMn7O12.19


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The main cause of the observed temperature dependence of quadrupole splitting is the gradual deformation of Mn2O6 and Mn3O6 octahedra with the development of the Jahn-Teller distortion. The satisfactory fit of the Mössbauer spectra in the whole paramagnetic temperature range, including the transition point of TOO, with only two Fe1 and Fe2 doublets implies that a percolative-type transition is not the case for the AMn7O12 system. Each individual grain of a sample would consist of a mixture of Jahn-Teller distorted and undistorted octahedra for a percolative transition. In Mössbauer spectra, it would manifest by additional splitting of doublets. In addition, the absence of hysteresis and continuous temperature dependence of quadrupole splitting, ∆1 and ∆2, is characteristic of a second-order phase transition.51 The form of DSC anomalies (on heating), especially for CaMn7O12 and SrMn7O12 (Figure 1), resembles an (inverted) λ-type anomaly, and is typical for second-order phase transitions. For example, very similar DSC anomalies were observed in YVO3 at a second-order orbital-ordering transition (TOO = 200 K).52 Because the values were calculated using crystallographic parameters of the modulated CaMn7O12 structure quite good agreement between the ∆iexp and values (Figure 10) can serve as an independent confirmation of the proposed structural model. Moreover, this agreement clearly indicates that the experimentally observed temperature dependence of quadrupole splitting for the Fe1 and Fe2 doublets is associated with the structural modulation in CaMn7O12. It should be noted that because of the narrowness of distributions pi(∆), which gives only a slight broadening (∆W ≤ 0.05 mm/s) of Mössbauer lines, one cannot go back from the experimental pi(∆) profile to the shape of the ∆mod(t) modulation, as the reciprocal transformation is not unique.

Conclusion In conclusion, we found structural modulation transitions at low temperatures in all members of the AMn7O12 family with A = Cd, Ca, Sr, and Pb. Surprisingly, the modulation is incommensurate in CaMn7O12 and SrMn7O12; while it is commensurate in CdMn7O12 and PbMn7O12, and can be described as a transition from space group R3 to space group P-3 with the same unit cell dimensions. Mössbauer spectroscopy showed that the quadrupole splitting noticeably increases below the structural modulation transitions, and we quantitatively explain this increase in CaMn7O12.



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Acknowledgements This work partially was supported by World Premier International Research Center Initiative (WPI Initiative, MEXT, Japan) and Russian Foundation for Basic Research (RFBR No. 14-03-00768). The synchrotron radiation experiments were performed at the NIMS synchrotron X-ray station at SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (Proposal Numbers: 2015A4502 and 2015B4504).

Supporting Information: The Supporting Information is available free of charge on the ACS Publication website at DOI: . Structural parameters of SrMn7O12 and PbMn7O12 at 113 and 295 K; temperature dependence of lattice parameters, details of some DSC, synchrotron XRPD, and Mössbauer data (PDF).


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Table 1. Structure Parameters, Bond Lengths, and Bond-Valence Sum (BVS)38 of CaMn7O12 and PbMn7O12 at Room Temperature. CaMn7O12 PbMn7O12 a (Å) 10.45891(2) 10.52100(2) c (Å) 6.34262(1) 6.40946(1) 3 V (Å ) 600.8588(6) 614.4218(10) 0.62(4) / 2.01 0.470(7) / 2.43 B(A) (Å2) / BVS1 B(Mn1) (Å2) / BVS2 0.732(12) / 2.93 0.506(12) / 2.81 2 B(Mn2) (Å ) / BVS2 0.559(13) / 3.25 0.324(13) / 3.14 2 B(Mn3) (Å ) / BVS2 0.52(3) / 3.99 0.38(3) / 4.01 BVS3(Mn3) 3.92 3.93 x(O1) 0.2235(2) 0.2288(3) y(O1) 0.2740(2) 0.2807(3) z(O1) 0.0811(2) 0.0798(4) B(O1) 0.64(3) 0.57(5) x(O2) 0.34091(17) 0.3441(2) y(O2) 0.52227(16) 0.5225(2) z(O2) 0.3425(3) 0.3348(4) B(O2) 0.50(3) 0.10(5) Rwp (%) 2.28 2.81 Rp (%) 1.42 1.63 2.49 3.97 RB (%) RF (%) 4.73 2.65 A-O2 (Å) ×6 2.576(2) 2.648(2) A-O1 (Å) ×6 2.691(2) 2.769(3) Mn1-O2 (Å) ×2 1.905(2) 1.932(2) Mn1-O1 (Å) ×2 1.915(2) 1.933(2) Mn1-O1 (Å) ×2 2.717(2) 2.672(3) Mn1-O2 (Å) ×2 2.816(2) 2.782(2) Mn2-O1 (Å) ×2 1.891(2) 1.895(3) Mn2-O1 (Å) ×2 2.041(2) 2.068(3) Mn2-O2 (Å) ×2 2.051(2) 2.063(2) Mn3-O2 (Å) ×6 1.911(2) 1.909(2) Space group R-3 (No 148), Z = 3. A cations (A = Ca and Pb) occupy the 3a site (0, 0, 0); Mn1 – 9e site (½, 0, 0); Mn2 – 9d site (½, 0, ½); Mn3 – 3b site (0, 0, ½); O1 and N

O2 – 18f site (x, y, z). The occupation factor of all the sites is unity. BVS =

∑ν

i

, νi =

i =1

exp[(R0 − li)/B], N is the coordination number, B = 0.37, R0(Ca2+) = 1.967 and R0(Pb2+) = 2.112 for BVS1, R0(Mn3+) = 1.760 for BVS2, and R0(Mn4+) = 1.753 for BVS3.



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Table 2. Structure Parameters, Bond Lengths, and Bond-Valence Sum (BVS) of Cubic Modifications of CaMn7O12 and PbMn7O12 at High Temperatures. CaMn7O12 PbMn7O12 T (K) 490 420 a (Å) 7.38162(1) 7.43576(1) 3 V (Å ) 402.2118(6) 411.1278(6) 1.34(3) / 1.96 1.015(7) / 2.24 B(A) (Å2) / BVS1 B(Mn1) (Å2) / BVS2 1.174(8) / 2.92 1.132(14) / 2.94 2 B(Mn2) (Å ) / BVS2 0.755(5) / 3.36 0.590(11) / 3.21 y(O) 0.31072(11) 0.3189(2) z(O) 0.17662(12) 0.1829(2) B(O) (Å2) 1.118(12) 0.87(4) Rwp (%) 2.12 3.05 Rp (%) 1.43 1.64 RB (%) 3.93 4.02 RF (%) 9.10 3.21 A-O (Å) ×12 2.638(1) 2.734(2) Mn1-O (Å) ×4 1.911(1) 1.914(2) Mn1-O (Å) ×4 2.766(1) 2.715(2) Mn2-O (Å) ×6 1.975(1) 1.992(1) Space group Im-3 (No 204), Z = 2. A cations (A = Ca and Pb) occupy the 2a site (0, 0, 0); Mn1 – 6b site (0, ½, ½); Mn2 – 8c site (1/4, 1/4, 1/4); O – 24g site (0, y, z). The occupation factor of all the sites is unity.


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Table 3. Lattice Parameters of CdMn7O12, SrMn7O12, and PbMn7O12 at Different Temperatures. Temperature (K) 113 154 193 235 295 418 443 465 488 508 528 543 563 583 113 193 295 113 295

a (Å) CdMn7O12 10.43306 10.43771 10.44307 10.44827 10.45507 10.46119 10.46239 10.46336 10.46360 7.37622 7.37751 7.37883 7.38012 7.38146 SrMn7O12 10.48622 10.49070 10.49970 PbMn7O12 10.50568 10.52100

c (Å) 6.33939 6.33708 6.33591 6.33379 6.33336 6.33877 6.34049 6.34257 6.34542

6.38026 6.37974 6.38104 6.40980 6.40946



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Table 4. Hyperfine parameters of CdMn6.9657Fe0.04O12 (I), CaMn6.96557Fe0.035O12 (II), and SrMn6.9257Fe0.08O12 (III) at different temperatures. Sample

T (K)

I

90

297

II

Sites

δ (mm/s)

∆ (mm/s)

W (mm/s)

I (%)

Fe1

0.48(1)

0.73(1)

0.35(1)*

73(1)

Fe2

0.48(1)

0.31(1)

0.35

27(1)

Fe1

0.37(1)

0.66(1)

0.27(1)*

73(1)

Fe2

0.38(1)

0.10(1)

0.27

27(1)

Fe1

0.48(1)

0.70(1)

0.29(1)*

73(1)

Fe2

0.48(1)

0.26(1)

0.29

27(1)

Fe1

0.36(1)

0.59(1)

0.29(1)*

73(1)

Fe2

0.37(1)

0.10(1)

0.29

27(1)

Fe1

0.49(1)

0.69(1)

0.31(1)*

69(1)

Fe2

0.50(1)

0.28(1)

0.31

31(1)

Fe1

0.37(1)

0.57(1)

0.28(1)*

67(1)

Fe2

0.38(1)

0.18(1)

0.28

33(1)

90

297

III

81

297

δ is an isomer shift, ∆ is quadrupole splitting, W is linewidth, and I is a relative intensity. * W parameters were constrained to be the same for the Fe1 and Fe2 doublets.


Page 23 of 34

-0.080

Cd

Heat flow (W/g)

Pb -0.085

265 K 254 K

Sr 294 K

-0.090

Ca (a) heating

258 K

-0.095 0.120

(b) cooling Pb

0.115

Heat flow (W/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.110 0.105

Cd

0.100

Ca

0.095

Sr

0.090 0.085 0.080 180

230

280

330

380

Temperature (K)

Figure 1. (a) Fragments of differential scanning calorimetry curves of CdMn7O12 (black), CaMn7O12 (green), SrMn7O12 (red), and PbMn7O12 (blue) on heating (a) and cooling (b) with a rate of 10 K/min. Second runs (among three runs) are shown. Phase transition temperatures TOO are marked by arrows. Small kinks below 185 K on cooling curves are atrifacts because a DSC system cannot support a cooling rate of 10 K/min below this temperature.


113 K

(1 5 1.9215)

5

Page 24 of 34

(3 3 2.0785)

CaMn7O12

(1 5 0.0785)

6

Intensity (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(1 4 2.0785) (2 4 1) (2 2 3)


4 193 K

3 2

235 K

1

295 K

*

*

*

R-3

0 23

24

25

26

27

28

2θ (deg): λ = 0.70014 Å Figure 2. Fragments of experimental synchrotron XRPD patterns of CaMn7O12 at 113, 193, 235, and 295 K. The bars show possible Bragg reflection positions of CaMn7O12 in the R-3 model (at 295 K); possible Bragg reflection positions expected for a commensurate P-3 model are also shown at 113 K. Indexes (h k l) of some reflections are given. Asterisks denote some artifact reflections. XRPD patterns were shifted for clarity; therefore, peak intensities (in %) relative to ‘background’ intensities should be considered (the strongest peak at each temperature has 100 % intensity).


Page 25 of 34

1.3

Intensity (counts/106)

(a) CaMn7O12 T = 295 K

0.03

0.8

0.01

-0.01 50

52

54

56

58

60

60

62

64

66

68

70

0.3

-0.2

(b) CaMn7O12 T = 490 K Intensity (counts/106)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.02

1.0 0.01

0.6 0.00

0.2

-0.2 5

15

25 35 2θ (deg): λ = 0.70014 Å

45

55

Figure 3. Experimental (black crosses), calculated (red line), and difference (blue line) synchrotron XRPD patterns of CaMn7O12 at (a) 295 K and (b) 490 K. The bars show possible Bragg reflection positions of CaMn7O12. The inserts show enlarged fragments.



10.470

(a)

CaMn7O12

Lattice Parameter a (Å)

10.465 10.460

CdMn7O12 10.455 10.450 10.445 10.440 10.435 10.430 6.350

(b)

CaMn7O12

6.348

Lattice Parameter c (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

R-3

6.346 6.344

R-3(00γ)0

6.342 6.340 6.338

R-3

6.336 6.334 6.332 100

P-3 CdMn7O12 200

300

400

500

Temperature (K)

Figure 4. Temperature dependence of (a) the a lattice parameter and (b) the c lattice parameter in CaMn7O12 (green squares) and CdMn7O12 (black circles).


Page 26 of 34

Page 27 of 34

604

CaMn7O12

(a) 603

Im-3

V (Å3)

602

R-3

601

R-3(00γ)0

CdMn7O12

600 599 598

P-3

597

90.40

(b)

90.35

Pseudo-cubic angle (deg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Cd2+

90.30 90.40

90.25 90.20 90.15

Ca2+

90.35

Sr2+

90.30

90.10

90.25

90.05

90.20

90.00

90.15

Pb2+ rXII(A2+) (Å) 1.3

89.95 100

200

1.4

300

1.5

400

500

600

Temperature (K)

Figure 5. (a) Temperature dependence of the unit cell volume (V for the P-3 and R-3 phases and 1.5V for the Im-3 phase) in CaMn7O12 (green squares) and CdMn7O12 (black circles). (b) Temperature dependence of pseudo-cubic angle, αc,32 in CaMn7O12 (green squares) and CdMn7O12 (black circles). The inset shows dependence of αc on the A2+ ionic radius (A2+ = Ca, Cd, Sr, and Pb) at RT. cos(αc) = [13a2/(8c2)]/[1+3a2/(4c2)], where a and c are the lattice parameters (in the hexagonal setting).32


Page 28 of 34

(1 5 1.9235)

(3 3 2.0765)

SrMn7O12

(1 5 0.0765)

4

113 K

3 193 K

2 (2,4,1) (2,2,3)

Intensity (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(1 4 2.0765)


1

295 K

R-3 Mn2O3

0 23

24

25

26

27

28

2θ (deg): λ = 0.70014 Å Figure 6. Fragments of experimental synchrotron XRPD patterns of SrMn7O12 at 113, 193, and 295 K. The bars show possible Bragg reflection positions of SrMn7O12 in the R-3 model and Mn2O3 impurity; note that cubic Mn2O3 becomes orthorhombic at low temperatures (for simplicity, Bragg reflections of Mn2O3 are given in space group Ibca).39 Indexes (h k l) of some reflections are given.


7

(3 3 2) (1 1 4)

(1 5 0) (1 3 3)

8

(2 4 1) (2 2 3)

CdMn7O12

113 K

P-3

6

Intensity (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(3 3 1) (1 4 2)

Page 29 of 34

154 K

5 4

193 K

3 235 K

2 295 K

1 R-3

0 23

24

25

26

27

28

2θ (deg): λ = 0.70014 Å Figure 7. Fragments of experimental synchrotron XRPD patterns of CdMn7O12 at 113, 154, 193, 235, and 295 K. The bars show possible Bragg reflection positions of CdMn7O12 in the R-3 model (at 295 K) and in the P-3 model (at 113 K). Indexes (h k l) of some reflections are given. Regions containing some artifact reflections are omitted.



10

8

(3 3 2)

(1 4 2)

(1 5 0)

PbMn7O12

9

113 K

P-3

6

Mn2O3

(2 2 3)

(2 4 1)

7

Intensity (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 34

5

295 K

4

R-3 Mn2O3

3 2

420 K

1

Im-3

0 23

Mn2O3

24

25

26

27

28

2θ (deg): λ = 0.70014 Å Figure 8. Fragments of experimental synchrotron XRPD patterns of PbMn7O12 at 113, 295, and 420 K. The bars show possible Bragg reflection positions of PbMn7O12 in the Im-3 model (at 420 K), the R-3 model (at 295 K), and the P-3 model (at 113 K) and Mn2O3 impurity; note that cubic Mn2O3 becomes orthorhombic at low temperatures.39 Indexes (h k l) of some reflections are given.


Page 31 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 9.

57

Fe Mössbauer spectra of CaMn6.96557Fe0.035O12 (left), SrMn6.9257Fe0.08O12

(middle), and CdMn6.9657Fe0.04O12 (right) at different temperatures. Dots are experimental points, black lines are the fitting results; contributions from the Fe1 and Fe2 doublets are shown by blue and green lines, respectively. The line at the bottom shows the difference between the experimental and calculated curves.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 10. (Up) Temperature variations of the quadrupole splitting, ∆1(T) and ∆2(T), for the Fe1 and Fe2 doublets. (Down) The ∆iexp(T) - ∆ith(T) curves for the Fe1 and Fe2 doublets (∆iexp(T) ≡ ∆i(T)) at different temperatures(see text for details).


Page 32 of 34

Page 33 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 11. (Left) The calculated quadrupole splitting modulations ∆1mod(t) (up) and

∆2mod(t) (down) in CaMn6.96557Fe0.035O12 for the Mn2 and Mn3 sites. Solid lines correspond to the Fourier approximation (equation 4, see text). (Right) Logarithmic representation of distributions p1(∆) and p2(∆) calculated using the amplitudes of Fourier harmonics and corresponding average values of quadrupole splitting, and (red arrows).



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure For Table of Contents Only

Cd: TOO = 254 K ⇒ P3

R3

Ca: TOO = 258 K ⇒ R3(00γ)0 Sr: TOO = 265 K ⇒ R3(00γ)0 Pb: TOO = 294 K ⇒ P3


Page 34 of 34

Low-Temperature Structural Modulations in CdMn7O12, CaMn7O12

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